ROME (Reuters) - Italy set out plans on Monday to help thousands of people staying in hotels and temporary accommodation in central Italy after the fiercest earthquake in decades struck regions already rocked by repeated tremors in the past two months.

No deaths or critical injuries have been reported after Sunday's quake, measured at 6.6 magnitude by the U.S. Geological Survey, partly because many had fled their homes after a smaller quake nearby killed almost 300 people in August.

Prime Minister Matteo Renzi pledged to rebuild the stricken areas, deploy more emergency and administrative officials, and speed up the provision of containers for people to live in, before eventually building wooden houses.

"We will do everything necessary to put your towns back together," Renzi said at a news conference after a meeting with Italy's reconstruction commissioner and civil protection chief.

Renzi said the exact number of people who had been evacuated was still not clear, 36 hours after the strongest quake in Italy since one of 6.9 magnitude killed 2,735 near Naples in 1980.

Italy's civil protection authority said more than 4,500 people had been moved to hotels on the Adriatic Coast and around Lake Trasimeno, close to the university city of Perugia.

A further 10,000 had been put up in emergency centres in the Umbria and Marche regions, the authority said, adding to thousands already forced out of their homes by August's quake.

Italy had submitted a budget plan to the European Commission before the latest strong seismic activity started on Oct. 26, citing reconstruction after August's quake among the reasons for increasing its structural budget deficit.

An EU official said Italy's response to the Commission's concerns about its budget had been "un-constructive", but Renzi brushed off the suggestion there was any tension with Brussels.

"There is no problem with Europe," Renzi said. He said there was already enough money in the draft budget to cover the plans unveiled on Monday, but this could be reviewed.

CULTURAL HERITAGE

Aerial video footage released by the fire department showed long cracks running through the surface of Redentore Mountain near the epicentre close to the Umbrian walled town of Norcia.

In Norcia, firefighters inspected the damage around the 13th century Basilica of St. Benedict, which collapsed leaving only its facade standing, and the Cathedral of Santa Maria Argentea, whose belltower was severely cracked.

"We will try to rescue all the cultural heritage that has survived but we are right in the centre of seismic activity, the tremors are very, very intense," fireman Domenico De Vita said.

Reconstruction commissioner Vasco Errani said artistic and architectural treasures would be secured as soon as possible, and the government would focus on relaunching the local economy.

"We cannot leave a piece of the country at risk of being abandoned by its population," Errani said. "Without those territories, Italy would be something else."

Sunday's tremor was felt as far north as Bolzano, near the Austrian border, and in the southernmost region of Puglia.

Schools were closed on Monday in the capital Rome, whose mayor Virginia Raggi said checks were being carried out on buildings and the city's evacuation plan was being updated.

"Every crack, every fault that might emerge will be checked," she said. "We cannot delay any more."

Leading seismologist Gianluca Valensise warned on Sunday the earthquakes could go on for weeks along the central Apennine fault system.